where \(\phi \)  is the volume fraction and a convenient choice for the proportionality constant is
\(a=(\phi _M^{(0)})^{1/3}\) , \(\phi _M^{(0)}\)  being the maximum value
of \(\phi \)  for a given structure here taken as the fcc lattice [\(\phi _M^{(0)}=\phi _M^{\text{(fcc)}}=\sqrt{2}/6\) ].
We perform Monte Carlo simulations in the framework of the
parallel tempering scheme [1]} with a distribution of temperatures
bracketing the superparamagnetic (SPM)-ordered phase transition.
The set of temperatures \(\lbrace T_n\rbrace \)  is chosen either from a geometric distribution,
\(T_{n+1}/T_{n}=\text{const}\)  or according to the
constant entropy increase scheme [2]} which leads to a more homogeneous rate of
configuration exchange in the tempering scheme.
Periodic boundary conditions and Ewald summations are used with the so-called conducting external
conditions, according to which the system is embedded in a medium characterized by an
infinite permeability, which eliminates the shape dependent depolarizing effects [3]}, [4]}.
We emphasize that this is a necessary condition to get a spontaneous magnetization.
At this point, we refer a reader to the analysis and comments in [5]}, [6]}.
